The present invention relates to high phase order induction machines.
The AC induction motor has been known for 120 years, and high phase order (HPO) induction motors have been in research since the 1970. In this time, the induction motor has become the workhorse of industry. Basic analysis of induction motor systems generally centers upon the development of good equivalent circuit models of the machine. One of the basic simplifying treatments is to assume a ‘fully sinusoidal distributed winding’. For the purpose of the following discussion, such analysis will be taken as a given and not developed. Rather than focusing upon the rotating magnetic field and its interaction with the rotor and the stator windings, this disclosure will focus upon the rotating distribution of current flowing through the stator windings.
This rotating current distribution may be described as a superposition of rotating sinusoidal current distributions, each of which is subject to standard analysis as necessary. Thus the focus of this disclosure is the generation of the rotating current distribution, limits to the allowable rotating current distributions in high phase order motors, and defects in the actual rotating current distributions produced.
High phase order motors share most of the technology and design methodologies of conventional three phase motors. For example, the equations relating flux per pole, effective number of series turns, frequency, and voltage placed across the winding are exactly the same. With a few simple adaptations, tools used to design three phase motors may be used for HPO designs. The significant difference is that an HPO motor uses a larger number of electrically independent coils, driven by a larger number of differently phased sources. Derived from this core change are secondary changes in things such as desirable winding distribution, chording, number of turns per coil, etc.
The primary impetus for research into HPO motors has been to reduce the deleterious effects of drive harmonics on motor efficiency. Research into mesh connected HPO machines extends this to the intentional use of drive harmonics to enhance the use of inverter power electronics.
Briefly touching on the rotating magnetic field, in the ideal case the rotating magnetic field acts as a fixed distribution rotating about the axis of the motor. This implies that in the ideal case the current distribution must also have a fixed structure rotating about the axis of the motor. This ideal requires that current be defined at each and every position around the stator, and is thus not physically realizable. Real motors are built with finite numbers of stator conductors, usually localized in a smaller number of slots.
The ‘sampling theorem’ provides the means to deal with this situation.
This concept, well known in the field of digitized audio systems, simply states that a bandwidth limited continuous signal may be faithfully represented by a discrete sampling at sufficient but finite frequency. For example, a 0 to 20 kHz continuous audio signal may be faithfully represented by taking samples at a rate greater than 40 kHz. The continuous signal f(t) is present at an infinite number of ‘points in time’, however it may be faithfully represented and reconstructed from a sampled signal f(n), where the values are only known only at the ends of a finite number if intervals in time.
As applied to motor windings, one needs consider the distribution of current flow on the stator. This current distribution is a signal in space rather than in time, sampled by the stator windings. The stator winding, with its distribution in space and its magnetic coupling across the entire stator is in essence the ‘reconstruction filter’ required to apply the sampling theorem. The samples of the current distribution are themselves continuous time series, and this two-dimensional reconstruction in circumferential position and time creates the rotating current distribution.
The analysis of the rotating current distribution developed is most simply performed when the drive current time series consists of sinusoidal currents, where each supply leg produces an alternating current of the same amplitude and frequency, but with different phase. For the analysis of real non-sinusoidal drive current, the approach is to decompose the real current into a set of sinusoidal drive currents by harmonic analysis, analyze each separate sinusoidal component, and then sum the resultant single frequency rotating current distributions into a composite.
The nature of the sampling theorem requires a bandwidth limited signal. This means that frequencies present must lie within a specified limited range. Any frequency that is outside of this range will be aliased into the allowed limited range. When a signal outside of the representable range is sampled, and the resulting samples ‘reconstructed’ into a continuous signal, the output of the reconstruction must be within the allowable range. In the case of motor windings, the bandwidth limiting means spatial bandwidth limiting, in other words limits to the shape of the rotating current distribution.
As generally applied, the sampling theorem is used to describe time series where the duration of the series is much longer than the sampling interval. In the present application, the stator is circular, and thus both finite yet unbounded, and the current distribution reconstructed from the sampling is periodic, with a period constrained to the circumference. This greatly simplifies the analysis, a finite number of sample points are mapped onto a limited set of basis functions.
Harmonics present in drive current are equivalent to values sampled from a rotating current distribution with higher pole count fields present. These harmonic components not only have frequency values which are multiples of the fundamental drive current frequency, but these components have time displacement values which are the same as the fundamental time displacement value. Referred to the period of the harmonic component in question, the phase angle displacement is a multiple of the fundamental phase angle displacement.
In a conventional three phase stator winding, three values of current flow are defined by the external drive. These three values are distributed across the stator by the winding, and reconstruct a quite reasonable current distribution. However the three sample points restrict the possible bandwidth of the reconstruction. Any harmonics present in the drive current will reconstruct rotating current distributions which are restricted to those represented by the winding.
As a qualitative description, consider a two pole stator winding with a total of 6 phase bands. These carry the three phases and their respective inverses. Harmonic currents in the drive result in the following phase angle distributions about the stator:
TABLE 1a two pole stator winding with a total of 6 phase bandsHarmonicLEG1x2x3x4x5x6x7xA0000000C′603001806030018060B12024001202400120A′180180180180180180180C24012002401200240B′3006018030060180300
As may be simply observed, such a two pole winding can only develop a two pole rotating current distribution. Triplen harmonic currents will develop a stationary current distribution, however circuit arrangement will generally dictate that triplen harmonic currents cannot actually enter the machine. In this regard, Triplen is a technical term referring to harmonics which are odd multiples of three, and do not enter three phase machines. Similarly, most of the circumstances that create harmonics create far more odd order harmonics than even order harmonics.
Each harmonic is ‘excited’ by alternating current at the fundamental frequency multiplied by the harmonic order. Thus the standard results that 6n−1 harmonics result in contra-rotating current distributions, and that 6n+1 harmonics rotate in the forward direction, both at much higher speeds than the fundamental field.
Continuing the above example, consider a 9 phase stator in similar circumstances. This simplified example stator uses a full span coils, and has a total of 18 phase bands. Drive current is evenly distributed, with 40 degree phase difference between adjacent phases.
TABLE 2a 9 phase stator having full span coils with a total of18 phase bandsHarmonicLEG1x2x3x4x5x6x7x8x9x10x11xA00000000000F′202206026010030014034018020220B408012016020024028032004080G′60300180603001806030018060300C8016024032040120200280080160H′100203002201406034026018010020D120240012024001202400120240J′1401006020340300260220180140100E16032012028080240402000160320A′180180180180180180180180180180180F2004024080280120320160020040B′2202603003402060100140180220260G240120024012002401200240120C′2603406014022030020100180260340H28020012040320240160800280200D′30060180300601803006018030060J32028024020016012080400320280E′3401403001002606022020180340140Poles21461010614218214Direction−+−+−+−NR+−adj diff20−14060−100100−60140−2020−140
Several features of the rotating current distribution become quickly apparent once harmonics in the HPO stator are considered. First is that the 3rd, 5th, and 7th harmonics produce synchronous rotating current distributions, that is current distributions where the pole count is scaled with the harmonic order, and which thus rotate at the same speed as the fundamental current distribution. Second, the use of full span windings results in nearly pathological results for low even order harmonics. This interaction between winding span and even order harmonics will be expanded below.
Generally, adding phases permits harmonic current flows to construct harmonic rotating current distributions that carry higher frequency spatial components, permitting such harmonic rotating drive currents to beneficially drive the rotating machine.
It is common practice to use short pitch, distributed windings. These offer several significant benefits, in particular reducing the magnitude of spatial harmonic fields produced by the windings, reducing length in the end turns, and more evenly distributing the stator windings about the circumference of the stator. Winding distribution is quite simply a low pass filter technique, applied to the current distribution. This low pass filter more strongly impacts high frequency components of the rotating current distribution, selectively reducing spatial harmonic content.
When winding distribution is applied to high phase order windings, this low pass filtering effects both those spatial harmonics in the magnetic field structure which are inherent to the coils themselves, as well as any current distribution harmonics reconstructed by the several sampling points. The smoothing/low pass filtering means that the magnetic flux produced by a given amount of harmonic current flow is reduced, or in other words the inductance of the machine to these harmonic current flows. Winding distribution must be used cautiously when harmonic components are present in the drive current, as significant harmonic current may flow without producing any useful output.
Voltage is only defined between one location and another, generally two nodes of a circuit. Given a circuit of N nodes, N−1 voltage measurements are sufficient to define the relative potential of all of the nodes, and thus to completely determine the N*(N−1)/2 voltage measurements possible between any two nodes. Often because of system symmetry, many of these voltages will have the same magnitude, and be discussed in general terms. For example, in three phase systems we discuss line-line (V_ll) and line-neutral (V_ln) voltage.
Owing to the shared DC rail and internal circulating current, inverters may be considered wye connected sources, with a well defined phase to neutral voltage. When supplying a mesh connected load, the load voltage is given by:V_ll=V_ln*2*sin(/phi/2)
where /phi is the phase angle difference between connected phases. For conventional three phase systems, /phi is 120 degrees, and V_ll=V_ln*1.732.
In high phase order systems, the V_ll will be anywhere between 0 and 2 times V_ln.
As previously noted, given an HPO machine of sufficient phase count, harmonic drive currents will develop rotating current distributions which are synchronous with the fundamental rotating current distribution. Drive currents with phase angle difference similar to those of synchronized harmonics will produce rotating current distributions that may be used to operate the motor.
Changing between operation on one allowed harmonic to another results in a different phase angle difference /phi being placed across the motor windings. This results in a different relationship between V_ll and V_ln, in essence changing the effective number of series turns that the motor winding presents to the inverter. This may be used, for example, to increase the machine impedance, raise the required terminal voltage, and reduce the required drive current for low speed high torque operations.
Losses associated with maintaining an electromagnet are proportional to the circumference of the excitation coils. However the flux created by the excitation current scales as the cross section of the magnetic poles. Because circumference is proportional to the linear dimension, whereas cross section is proportional to the square of the linear dimension, as magnetic poles get larger the total flux maintained by a given amount of loss increases. In a given machine with fixed winding structure, this becomes quickly apparent; magnetizing losses tend to increase as pole count increases. This is somewhat mitigated by reduction in stator core losses, however in general a given machine becomes less efficient when operated in ‘harmonic’ mode with multiplied pole count. It is therefore desirable, when using ‘harmonic operation’ to use the smallest change in pole count.